Derivation of the bidomain equations for a beating heart with a general microstructure

Abstract

A novel multiple scales method is formulated that can be applied to problems which have an almost
periodic microstructure not in Cartesian coordinates but in a general curvilinear coordinate system.
The method is applied to a model of the electrical activity of cardiac myocytes and used to derive a
version of the bidomain equations describing the macroscopic electrical activity of cardiac tissue. The
treatment systematically accounts for the non-uniform orientation of the cells within the tissue and for
deformations of the tissue occurring as a result of the heart beat.